Find parametric equations for the line passing through the point (4,-7,-6) and orthogonal to the...

Question:

Find parametric equations for the line passing through the point {eq}(4,-7,-6) {/eq} and orthogonal to the plane {eq}2x-3y+z=5 {/eq}

Parametric Equations:

If {eq}y = f(x) \ and \ x = f(y) {/eq} express y and x in terms of t. {eq}x = g(t) , y= h(t) {/eq}. These are called as parametric equations.

Answer and Explanation:

Equation of plane {eq}2x-3y+z=5 {/eq}

The given plane has a normal vector {eq}(2,-3, 1). {/eq} Since the required line is perpendicular to the given plane, it is parallel to the vector {eq}(2,-3, 1) {/eq}. Further, since it passes through the point {eq}P = (4,-7,-6) {/eq}, its vector equation is {eq}(x, y, z) = (4,-7,-6) + t (2,-3,1) {/eq}. Its parametric equation is {eq}x = 4+2t, y = -7-3t, z = -6 + t {/eq}


Learn more about this topic:

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Parametric Equations in Applied Contexts

from Precalculus: High School

Chapter 24 / Lesson 6
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